Measuring the principal planes and effective focal length of an optical imaging system

Abstract

We present a simple method to measure the two principal planes and the effective focal length of an imaging optical system. It is based on measurements of transverse magnification of the image and both the object and image positions from two arbitrary reference points. A simple linear equation is derived to find the distances of the principal planes from the reference points, which enables the computation of the effective focal length. Experimentally, the method only needs a standard optical bench, thus avoiding the use of a nodal slide. The accuracy obtained for a practical example with an optical system composed of two achromatic doublets is smaller than 1 mm, or better than 2%, for all three measured values (two principal planes and the one effective focal length) as compared with the results of optical ray tracing performed with OSLO software.